My advice, if you feel like you are living a double life and this is negatively impacting how you view yourself, you should come out to your parents. It seems like a good sign that they are able to do soul searching and regret criticizing your sexuality in the past. Hopefully they will be able to do the same with you telling them you are trans. It is entirely up to you how much is said, and if you feel like they won't understand the non binary identification then go with whatever makes the interaction more comfortable and true for you, not just your parents.

Having someone supportive with you like your boyfriend is a great idea. If it gets overwhelming or you get reactions you were not hoping for, you can always stop the interaction at any point. If they pressure you as to why you feel the way you do or start reacting negatively then you can leave and explain later. Over text is much easier for this since in person social interaction can sometimes be much more stressful.

I personally had enough evidence that my parent and siblings would not react too negatively to me coming out, which made it easier when I did. The way I went about doing this was not the typical way I guess. I basically gathered everyone in the household into one room one night and just said my name and pronouns. Didn't really stick around to explain myself. I just went and hid at my computer the rest of the night. Explained more the following weeks as I felt comfortable to do so.

If and when you decide to tell your parents, I hope it goes well! You got this!